Solve an assignment problem online

Fill in the cost matrix of an assignment problem and click on 'Solve'. The optimal assignment will be determined and a step by step explanation of the hungarian algorithm will be given.

Fill in the cost matrix (random cost matrix):

Size: 3x3 4x4 5x5 6x6 7x7 8x8 9x9 10x10

Don't show the steps of the Hungarian algorithm
Maximize the total cost

This is the original cost matrix:

61	16	1	9	88
46	50	92	2	51
37	48	39	96	29
69	37	85	65	17
57	6	22	23	70

Subtract row minima

We subtract the row minimum from each row:

60	15	0	8	87	(-1)
44	48	90	0	49	(-2)
8	19	10	67	0	(-29)
52	20	68	48	0	(-17)
51	0	16	17	64	(-6)

Subtract column minima

We subtract the column minimum from each column:

52	15	0	8	87
36	48	90	0	49
0	19	10	67	0
44	20	68	48	0
43	0	16	17	64
(-8)

Cover all zeros with a minimum number of lines

There are 5 lines required to cover all zeros:

52	15	0	8	87	x
36	48	90	0	49	x
0	19	10	67	0	x
44	20	68	48	0	x
43	0	16	17	64	x

The optimal assignment

Because there are 5 lines required, the zeros cover an optimal assignment:

52	15	0	8	87
36	48	90	0	49
0	19	10	67	0
44	20	68	48	0
43	0	16	17	64

This corresponds to the following optimal assignment in the original cost matrix:

61	16	1	9	88
46	50	92	2	51
37	48	39	96	29
69	37	85	65	17
57	6	22	23	70

The optimal value equals 63.